Use our free GCF of Fractions Calculator tool to compute the GCF of 564/574, 512/309 i.e 4/177366 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/574, 512/309.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 564/574,512/309
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 564/574,512/309, numerators are 564,512
Denominators are 574,309
The GCF of 564,512 is 4 .
LCM of 574,309 is 177366.
The greatest common factor of 564/574,512/309 = [GCF of 564,512]/[LCM of 574,309]= 4/177366
Therefore, the GCF of 564/574,512/309 is 4/177366.
To find the highest common factor of 564,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 564,512 is 4.
Lets's calculate GCF of 564,512
2 | 564, 512 |
2 | 282, 256 |
141, 128 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 564,512 . The biggest common factor number is the GCF number.
So the greatest common factor 564,512 is 4.
Lets's calculate LCM of 574,309
Given numbers has no common factors except 1. So, there LCM is their product i.e 177366
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/177366
Therefore, the GCF of Fractions 564/574,512/309 is 4/177366
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 574,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(574,309) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(574,309) x common factors =1 x 1 = 1
LCM(574,309) = ( 574 × 309 ) / 1
LCM(574,309) = 177366 / 1
LCM(574,309) = 177366
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 564,512?
The HCF of 564,512 is 4
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 564/574, 512/309?
Answer: GCF of Numerators as per given numbers 564/574, 512/309 is
GCF of Numerators i.e. for 564,512 is 4
LCM of denominators i.e. for 574,309 is 177366.
Thus, GCF of Fractions is 4/177366.Finally, GCF of Fractions for 564/574, 512/309 is 4/177366.